The power in a transmitted signal is segregated between a carrier frequency (channel) and adjacent frequency bands (channels). All transmitted signal waveforms spill some power from the main lobe (the carrier frequency) into the adjacent channels. Filtering at the receiver minimizes the effects of the adjacent channel power during the demodulation and detection process. Although the adjacent channel power may be relatively small compared with the carrier frequency power, the adjacent channel power is a source of interference and signal quality degradation for other users operating in the same frequency band.
The frequencies adjacent the carrier can be segregated into 5 kHz channels (referred to as narrowband channels) and 25 kHz channels (referred to as wideband channels) for analysis of the adjacent channel power. The power emitted in the adjacent channels is computed by integrating the transmitted power spectral density (PSD) over the desired 5 kHz bandwidth or over a desired 25 kHz bandwidth. The center of the each channel is therefore offset by 5 kHz or by 25 kHz from the adjacent channel for the narrowband and wideband cases, respectively.
MIL-STD-188-181A, MIL-STD-188-182 and MIL-STD-188-183 define allowable limits of adjacent channel emissions (ACE) for all transmissions on US-owned ultra-high frequency (UHF) satellite communications (SATCOM) channels. The ACE requirements, which are specified for both 5 kHz narrowband channels and 25 kHz wideband channels, limit the amount of energy that can be spilled into adjacent (offset) channels above and below the main (carrier) transmitting channel (frequency).
The two primary modulation techniques recommended by the aforementioned MIL standards include a linear 50% shaped binary phase shift keyed (SBPSK, a form of BPSK) modulation and 50% shaped offset quadrature shift keyed (SOQPSK) modulation. These modulation techniques attempt to limit the sidelobe power by producing a modulating signal that has a continuous phase transition. The SOQPSK technique offers outstanding side lobe suppression that satisfies the MIL standard ACE requirements.
The 50% SBPSK modulating waveform recommended in MIL-STD-188-181A, however, may not provide sufficient ACE margin in the first two 5 kHz offset channels at a maximum data rate of 2400 bps, nor in the first two 25 kHz offset channels at a data rate of 9600 bps. With little margin over the requirements when 50% BPSK is employed, hardware limitations may further degrade ACE performance and cause out-of-spec operation.
A BPSK modulated carrier is characterized by inherently high side lobes (the first sidelobe is at only −13 dBc), as illustrated by the power spectral density of a BPSK modulated signal shown in FIG. 1. The energy spilled over into the first six 5-kHz channels, each marked by one of six horizontal bars in FIG. 1, far exceed the allowed emissions specified by the MIL-STD 188-181A.
SBPSK modulation reduces energy spillage in the adjacent channels by virtue of its low-level side lobes. When employed to modulate a carrier signal, SBPSK modulation linearly changes the carrier phase trajectory by 180 degrees over a time interval shorter than a bit period. In an embodiment where the time interval is zero, the resulting waveform is BPSK, i.e., an instantaneous 180 degree phase transition (a 180 degree phase transition in zero time). If the transition time is half a bit period, the modulation is referred to as 50% SBPSK. Thus a ratio of the phase transition time to the bit period represents the shape factor for the phase transition. Shape factors can range from zero to 100% of the bit period.
For BPSK or SBPSK phase transitions occur only when the data bits transitions from a one to a zero and from a zero to a one. The phase transitions from zero to 180 degrees (π radians) must alternate direction, i.e. if the previous phase transition was from zero to 180 degrees, the next phase transition, when it occurs, must be from zero to −180 degrees. This phase derotation must be maintained to avoid generating a frequency offset in the resulting signal. This rotation is depicted in FIG. 2 where sequence numbers 1 through 4 referring to a half circle denote the direction of phase transition between zero, π and −π for a data sequence of 1010.
The phase transitions for various SBPSK shape factors are depicted in FIG. 3 for a data stream with bit intervals of Tb and a bit rate of 1/Tb bits per second. A curve 20 represents the phase transitions for BPSK, a curve 22 represents the phase transitions for a 50% SBPSK (i.e., BPSK with a shaping factor of 50%, where the shaping factor designates a portion of the bit period during which the phase is changing) signal, a curve 24 represents the phase transitions for a 75% SBPSK signal and a curve 26 represents the phase transitions for a 100% SBPSK signal. The data stream is delayed by at least one bit period so that it can be determined whether a transition occurs at the next data bit and the transition shaped as desired if a transition occurs.
SBPSK modulation with any shaping factor is characterized by a single linear phase function, as can be seen from the phase transition straight lines in FIG. 3. Note that the phase transitions for the different shaping factors start at different times of the bit interval. For example, common BPSK presents no shaping and the bit transition is therefore instantaneous. A 50% SBPSK phase transition spans one-half of a bit interval, including a portion of both a first bit interval and a second bit interval. A first portion of the transition interval occurs during a last quarter of the first bit interval and a second portion of the transition interval occurs during a first quarter of the second bit interval. Thus the total phase transition time is one-half a bit interval. If a third bit is opposite polarity to the second bit, the 50% SBPSK phase transition spans a last quarter of the second bit interval and a first quarter of the third bit interval. Similarly, a 75% SBPSK phase transition spans ⅜ of the first bit interval and ⅜ of the second bit interval for a total transition time of ¾ of a bit interval. 100% SBPSK spans ½ of the first bit interval and ½ of the second bit interval for a total transition time of one bit interval.
The derivative of the linear phase functions of FIG. 3 with respect to time is a constant. Thus the modulated signal comprises a constant frequency during the phase transition portion of the bit interval.
Various waveforms corresponding to a prior art 50% SBPSK signal are shown in FIG. 4. FIG. 4 depicts a modulating data signal, a corresponding carrier phase trajectory, in-phase (I) and quadrature-phase (Q) signals and a modulated carrier, including phase transitions illustrated therein.
FIG. 5 illustrates a power spectral density plot 40 of a 50% SBPSK signal super-imposed on a power spectral density plot 42 of a BPSK signal. It is noted that the spectral confinement (reduced ACE) for SBPSK is visibly improved when compared with BPSK, especially for the second and subsequent signal side lobes.
Phase transitions and frequency deviations for a 50% SBPSK waveform modulated by a 10101010 bit sequence are shown in FIG. 6. As can be seen, the frequency deviation waveform resembles continuous-phase 3-ary FSK type modulation, with frequency deviations of 0, +Δƒ and −Δƒ.
A numerically controlled oscillator modulator (NCOM) can be used to digitally generate an SBPSK signal. Since the derivative of phase is frequency, linear phase transitions of SBPSK are implemented as step changes in frequency during the phase transition periods. The transitions can be linear phase transitions with positive slope or negative slope or the transitions can be constant-valued phase transitions. The carrier frequency is selected from among ƒc+Δf,ƒc−Δƒ or ƒc.
According to SBPSK modulation implemented with the NCOM the instantaneous frequency is read from a three element look-up table responsive to a bit rate clock interrupt and the value of the next bit (or symbol). Exemplary delta frequency values are set forth in FIG. 7 for 2400 bps and 9600 bps data rates and for 50%, 60%, 62.5%, 75%, 80%, and 100% shaping factors (SF).
FIG. 8 depicts the peak frequency deviation of 50%, 62.5%, and 75% SBPSK modulated carriers respectively for a data rate of 2400 bps as computed from the slope of the linear phase segments, as illustrated in FIG. 6, for example.
The peak frequency deviation of the SBPSK modulated carrier is the derivative of the carrier instantaneous phase with respect to time as described below:
      Δ    ⁢                  ⁢    f    =                    Δ        ⁢                                  ⁢        ω                    2        ⁢        π              =                  1                  2          ⁢          π                    ⁢                        ⅆ                      ϕ            ⁡                          (              t              )                                                ⅆ          t                    ⁢                          ⁢      Hz      
Since the instantaneous phase of the SBPSK modulated carrier is linear, the derivative is then equivalent to its slope. The frequency offset for SBPSK is then modeled by:
      Δ    ⁢                  ⁢    f    =            π              2        ⁢        π        ×        SF        ×                  T          b                      =                            π          ⁢                                          ⁢                      R            b                                    2          ⁢          π          ×          SF                    =                        R          b                          2          ×          SF                    where Rb=1/Tb is the bit rate and SF is the shape factor.
FIG. 9 depicts power spectral density simulation results for a 50% SBPSK shaping factor (a curve 60) and a 75% SBPSK shaping factor (a curve 62) for the 5 kHz narrow band channel at the 2400 bps data rate. Note the spectral confinement for a shape factor of 75% is better than the 50% shape factor especially at frequencies closer to the carrier frequency.
FIG. 10 depicts power spectral density simulation results for 50% (a curve 66) and 75% (a curve 67) SBPSK shaping factors for the 25 kHz wide band channel at a 9600 bps data rate. The spectral confinement for a 75% SBPSK shape factor is better than the 50% SBPSK shape factor especially at frequencies adjacent the carrier frequency. The power spectral density simulation for a 4800 bps signal reveals similar results.
FIG. 11 summarizes simulated and measured ACE performance for a 50% SBPSK signal in the 5 kHz channel at 2400 bps and the ACE requirements according to the MIL-STD-188-181A. It is clear that the ACE margin is narrow for this case especially in the 5 and 10 kHz adjacent channels. Therefore an improvement in ACE margin is desired.
FIG. 12 summarizes simulated and measured ACE performance for a 50% SBPSK signal in the 25 kHz channel at 4800 bps. In this case the ACE margin complies with the MIL-STD-188-181A requirements.
FIG. 13 summarizes simulated and measure ACE performance for a 50% SBPSK signal in the 25 kHz channel at 9600 bps. As shown, the ACE margin is narrow, especially in the 25 and 50 kHz adjacent channels. An improvement in the ACE margin is desired.
As can be seen from the above discussion and illustrative figures, The ACE performance improves with higher linear SBPSK shaping factors. However, it is known that these SBPSK shaping factors tend to reduce bit error rate (BER) performance. It is known that the 75% SBPSK shape factor yields a minimum of 5 dB of ACE margin over 50% SBPSK, at the expense of 1 dB over the 50% SBPSK implementation loss. Implementation loss refers to the affect of the shaping factor on bit error rate (BER) performance. For a fixed BER, the difference in the ratio of bit energy to noise energy (Eb/No) for a 75% shaping factor and a 50% shaping factor is the implementation loss. For example, to attain a BER of 10E-5, a 75% shaping factor signal requires an Eb/No value of 10 dB, while a 50% shaping factor signal requires an Eb/No value of 9 dB. Thus the implementation loss for the 75% shaping factor signal is 1 dB. FIG. 14 depicts measured values illustrating the effect of the shaping factor on the BER performance. A curve 100 depicts the BER performance of a theoretical BPSK transmitted signal. A curve 104 illustrates the BER performance for a BPSK signal demodulated by a coherent matched filter BPSK demodulator. BER curves generated by the same BPSK coherent demodulator for linear 50% SBPSK (curve 108), linear 62.5% SBPSK (curve 112) and linear 75% SBPSK (curve 116) transmitted signals are also depicted in FIG. 16. It can be seen that linear 50% SBPSK has about 1 dB implementation loss at a BER of about 10E-5. Linear 62.5% SBPSK adds an additional 0.5 dB loss, while linear 75% adds another dB of implementation loss over linear 50% SBPSK at a BER of about 10E-5.